Question: The following line passes through point $(7, 3)$ : $y = -\dfrac{6}{17} x + b$ What is the value of the $y$ -intercept $b$ ?
Answer: Substituting $(7, 3)$ into the equation gives: $3 = -\dfrac{6}{17} \cdot 7 + b$ $3 = -\dfrac{42}{17} + b$ $b = 3 + \dfrac{42}{17}$ $b = \dfrac{93}{17}$ Plugging in $\dfrac{93}{17}$ for $b$, we get $y = -\dfrac{6}{17} x + \dfrac{93}{17}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(7, 3)$